(z^2 – I)/(2 z^2 + 2 I )

Tufts Math professor Moon Duchin asked me to come up with a simple way for her class to use Mathematica to visualize functions of complex variables for her Complex Analysis class.

Each coordinate in the plane, can be mapped onto a complex number, e.g. (1,1) maps to 1+i. A complex function  is something that takes a complex number as input and spits out another complex number as output. The Mathematica program applies a complex function to each point in the complex plane and plots a color according to the argument of the number returned.

We invite you to download the mathematica notebook to try and use yourself.

Some sample plots are displayed below.


(z^2 – I)/(2 z^2 + 2 I ) – 1/2



Riemann Zeta function


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